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More precisely, for some ε>0, the objective is to find a matrix X∈[ 0,1] M×N or, equivalently, a vector (tilde {boldsymbol {x}}=text {vec}(mathbf {X} in,[!0,1]^{NM}) that solves the following problem begin{array}{*{20}l} text{min.} &sum_{l in {mathcal{L}}} left(c_{l}frac{logleft(1+epsilon^{-1} ~ boldsymbol{t}_{l}^{T} tilde{boldsymbol{x}}right)}{logleft(1+epsilon^{-1}right)} right.
One hopes then to find a matrix factorization which uncovers the network structure and simultaneously respects the label information of the labeled data.
A training dataset was used for each bootstrap in order to find a matrix score for the top 10 pairs of pathways with the best AUC value between NS versus BC samples (Random Forest classification).
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While these LR algorithms aim to find a unimodular matrix such that the channel matrix is more orthogonal.
For solving the problem with the PCG, the most important thing is to find a preconditioning matrix that makes the system matrix have low condition number.
Non-negative matrix factorization [15, 16] attempts to find a mixing matrix (with sparse weights [17, 18]) and a source matrix with non-negative elements so that the reconstruction error is minimized.
The problem we need to solve to find a signature matrix is formulated as follows: Signature matrix inverse eigenvalue problem (SMIEP).
According to modal theory, for each one Jacobian matrix (J) it is possible to find a Modal matrix (M) whose rows supply information of the metabolic pools at each time scale, see methods section.
Such a finding seems to indicate that, in order to find a consensus matrix which captures well the inherent structure of the dataset, one needs a sensible number of connectivity matrices.
We consider the nonnegative inverse eigenvalue problem with partial eigendata, which aims to find a nonnegative matrix such that it is nearest to a pre-estimated nonnegative matrix and satisfies the prescribed eigendata.
A systematic approach to find a common matrix P for TSS fuzzy system is presented first, where system matrix Ai is decomposed into proportional part Ãi and the remainder ΔAi.
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Justyna Jupowicz-Kozak
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